Process for finishing fibrous materials, and compositions for use therein



3,057,675 Patented Oct. 9, 1962 free This invention relates to a process for imparting a finish to fibrous materials, particularly textile materials and to compositions used in said process.

According to the present invention there is provided a process for the treatment of fibrous materials which are capable of reacting with compounds comprising mobile halogen atoms which process comprises impregnating the fibrous material with a liquid-containing preparation containing a 1,3,5-triazine compound in which the triazine ring has at least one nuclear halogen substituent and at least one nuclear substituent comprising a hydrocarbon radical containing more than 7 carbon atoms, and fixing the said triazine compound on the fibrous material by treatment with an acid-binding agent.

Fibrous materials which can be advantageously finished by the aforesaid process include animal fibers such as wool or silk, semi-synthetic fibers such as cellulose acetate fibers, and fully synthetic fibers such as polyamide fibers, for example those derived from e-caprolactam or from adipic acid and hexamethylenediamine. The process has proved particularly advantageous when applied to cellulose-containing fibers such as linen or cotton and to fibers consisting of regenerated cellulose, such as viscose rayon or staple fiber.

The triazine compounds employed in the present process comprise at least one 1,3,5-triazine ring. There is directly attached to the said triazine ring at least one halogen atom, and at least one substituent comprising a hydrocarbon radical containing more than 7 carbon atoms. The said hydrocarbon radical may be attached directly to the said ring but preferably is linked thereto through a bridge member containing or consisting of at least one hetero atom. Thus the 1,3,5-triazine ring may be substituted in 2,4,6-position by (a) two halogen atoms and one substituent containing the hydrocarbon radical of more than 7 carbon atoms,

(b) one halogen atom and two substituents containing hydrocarbon radicals of more than 7 carbon atoms, or

() one halogen atom, one substituent containing a hydrocarbon radical of more than 7 carbon atoms, and one other substituent of any form.

Chlorotriazine compounds are preferably employed. The hydrocarbon radical preferably contains 12 to 22 carbon atoms. It may be branched or unbranched, saturated or unsaturated. In addition, it may be attached to the triazine ring through, for example, a sulfur atom, an oxygen atom or, preferably, through a nitrogen atom. In the last-mentioned case, the substituent corresponds, for example to the formula:

( R-ITI- in which R represents an aliphatic hydrocarbon radical containing at least 8 carbon atoms, and R an alkyl radical, which may also contain 8 or more carbon atoms, or a hydrogen atom. The monoor dichlorotriazine compounds containing the radical of such an aliphatic amine preferably correspond to the formula:

K R-N-C N in which R represents an aliphatic hydrocarbon radical, preferably an alkyl radical containing from 16 to 22 carbon atoms, R a hydrogen atom or an aliphatic hydrocarbon radical, and X a chlorine atom or an amino group, for example an H N-group or a group of the formula:

atoms may alternatively be attached to the triazine ring through a bridge containing more than one hetero atom,

for example one containing an alkylene group between 1 two hetero atoms. Suitable examples are substituents of the formulae:

in which R has the meaning assigned to it above, and A represents an alkylene radical, for example an ethylene or propylene radical, or a phenylene radical.

In Case 0 referred to above, the triazine compound contains, in addition to the halogen atom and the substituent containing the aliphatic hydrocarbon radical of 8 or more carbon atoms, a further substituent of any form, for example a hydroxyl group, an amino group, an alkoxy group, e.g. a methoxy group, an aryloxy group, e.g. a phenoxy group or an aryl-mercapto group, e.g. a phenyl-mercapto group, optionally further substituted in the aryl nuclei, or a radical attached directly to the triazine nucleus.

Particularly valuable for the present process are the triazine compounds of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical, the radical R containing at least 8 carbon atoms, and n, p, q, and r each represent a whole number of at most 2. Thus the compounds of the Formula VIII in addition to the high molecular radical R may contain one, two or three further aliphatic hydrocarbon radicals and three, two or one hydrogen atoms bound to the nitrogen atoms. The monochloro- 1,3,5-triazine compounds may preferably correspond to the formula in which at least one and at the most two Rs represent alkyl radicals containing 16 to 22 carbon atoms and the remaining Rs represent hydrogen atoms.

The triazine compounds employed in the present invention may be prepared, by methods known per se from the literature, from cyanuric halides, such as cyanuric bromide or preferably cyanuric chloride and alcohols, mercapta-ns, phenols, thiophenols or amines. Compounds containing hydrocarbon radicals directly attached to the triazine ring are obtained by reacting cyanuric halide with alkyl-, cycloalkyl-, aralkylor aryl-magnesium halides. Compounds of Formula II in which X represents a chlorine atom are preferably prepared by condensation of cyanuric chloride with one or more amines of the formula:

R-NH

in which R and R have the meanings assigned to them above, in the molecular ratio 1:1, in organic solvents at low temperature.

In the process of the present invention the impregnation of the fibrous material is effected with a liquid-containing preparation which contains the triazine compound. Thus, for example, solutions of the compounds in inert organic solvents (i.e. those not reacting with halogen atoms of the triazine compounds), such as carbon tetrachloride, dichloroethane, methyl ethyl ketone, benzene, xylene, perchloroethylene and petroleum hydrocarbon, may be employed.

Alternatively, and more especially in the case of the triazine compounds of Formula II, the impregnating liquid may be an aqueous emulsion of the triazine compound. The triazine compounds are not liquid at room temperature, so that to formulate the emulsions it is preferable to dissolve the triazine compound in an inert solvent, for example chlorobenzene or a dichlorobenzene, and to emulsify the resulting solution in water. However, only a small quantity of solvent is generally required in relation to the quantity of the triazine compound, so that the mixture of triazine compound and 501- vent is less a solution in the usual sense than a melt.

For the preparation of the emulsions, emulsifiers may be employed but in order to avoid saponification of the triazine compounds (exchange of halogen atoms for hydroxyl groups) it is important that the emulsifiers should not be more than at most mildly alkaline. Either ionic or non-ionic emulsifiers may be employed. The latter class includes, in particular, polyglycol compounds, for example polyglycol ethers of aliphatic alcohols of high molecular weight. Advantageously, water-soluble poly vinyl alcohol or a polypeptide-containing substance, such as gelatine, may be included as a thickening agent, preferably in addition to a polyglycol compound. Furthermore, the addition of a condensation product of naphthalenesulfonic acid and formaldehyde is recommended, the result of which is that a fine emulsion of the organic liquid (discontinuous phase) in the aqueous phase (continuous phase) rapidly forms during the stirring of the two phases.

Further agents for the finishing of the fibrous materials may be added to the aforesaid preparations, for example dressing agents, such as agents which are capable of exerting a similar action to the triazine compounds.

Examples are agents capable of imparting a soft handle to the textile material or water-repelling agents such as wax-like substances, e.g. paraffin wax, chloro-paraffin waxes, or a fusable polyalkylene such as polymerized ethylene, propylene or isobutylene. The wax-like substances may be simply added to solutions of the triazine compounds in organic solvents or, when the preparations are emulsions, they may be dissolved in the organic liquid of the emulsion together with the triazine compound. They may also be dissolved in an organic solvent separate- 1y from the triazine compounds, whereby emulsions comprising two different discontinuous phases may be produced.

The triazine compound content of the preparations may vary within wide limits. For example, preparations may be directly prepared in which the concentration is, for example, from 3 to 10 parts of triazine compound in parts of the preparation.

Generally speaking, however, it is more advantageous to make preparations having a high triazine compound content, which are then diluted before use, for example by addition of a further quantity of solvent to the concentrated solution or by addition of water to the concentrated emulsion.

The fibrous materials may be impregnated in any usual manner, for example by dipping, spraying or coating, advantageously at room temperature or at most at a slightly elevated temperature. It is particularly desirable to impregnate woven fabrics with the preparations on :1 padding machine.

The impregnation is followed, if desired after intermediate drying at room temperature or at most at slightly elevated temperature, by treatment with an acid-binding medium, with the object of inducing chemical reaction between the halogenotriazine compound and the fibrous material, so that the triazine compound becomes attached (in homoeopolar fashion) to the fibrous materinl, for example to the oxygen atoms of a cellulosic fibrous material.

This treatment may advantageously be carried out with dilute aqueous sodium carbonate solution. Temeratures of at most 30 to 40 C. are generally sufiicient for the treatment, e.g. in the case where dichlorotriazine compounds are employed.

The treatment of the fibrous materials by the process of the present invention generally produces a water-repelling efiect and at the same time imparts a soft handle to the fibrous material.

In the following examples, where not otherwise stated, the parts are indicated by weight, the percentages by weight, and the temperatures in degrees centigrade, as in the foregoing description. Measures by weight and by volume are related as grams to cubic centimeters.

EXAMPLE 1 (A) Preparation of the triazine c0mpozmd.-IO0 parts (0.362 mol.) of a commercial stearylamine containing 93% of octadecylamine, 6% of hexadecylamine and 1% of octadecenylamine are dissolved in 2,000 parts of acetone at 50 to 60. On cooling to 2 to 5 with stirring, a fine suspension is obtained, to which is slowly added a similarly prepared suspension of 67 parts (0.52 mol.) of cyanuric chloride and 320 parts of acetone. It is to be noted that the temperature of the mixture should not exceed 5. 3 hours after the introduction of the cyanuric chloride suspension, the temperature is allowed to rise to 10, and a solution consisting of parts of water and 19.2 parts of sodium carbonate at 5 is added. The mixture is then further stirred for 18 hours at room temperature. The reaction mixture has a pH value of 5 to 6. It is then suction-filtered and the filtrate is washed first with like-warn and then with cold water, until the filtrate has a completely neutral reaction. After drying in vacuo at 40, about 126 parts of a crystalline substance, M.P. 7273 are obtained.

Instead of the aforesaid amine mixture, any other primary or secondary alkylamine of relatively high molecular weight may be employed. Thus, for example, there is obtained from 170 parts of a commercial dialkylamine, 75% of the alkyl radicals of which contain 18 carbon atoms, and 25% contain 16 carbon atoms, a reaction product which, after recrystallization from alcohol, gives about 191 parts of a well-crystallized substance melting at 126-135 Unsaturated amines, such as octodecenylamine (oleylamine) or an amine mixture prepared from coconut oil, do not give any Well-crystallized products.

(B) Preparation of emulsions-In an open stirrertype vessel, 3 parts of an emulsifier obtained by the addition of 80 mol. of ethylene oxide to 1 mol. of oleyl alcohol and 1.2 parts of a condensation product of naphthalene sulfonic acid and formaldehyde, neutralized with aqueous sodium hydroxide solution, are heated at about 70 with 30 parts of an approximately aqueous polyvinyl alcohol solution having a viscosity of 7 /3 centipoises at 20. 5.8 parts of water are then added to the solution, and 40.5 parts of a melt, heated at about 90, of 3.7 parts of chlorobenzene and 36.8 parts of the triazine derivative, (prepared as under A) are poured into the solution. The mixture is then very rapidly stirred until an emulsion is formed. 26 further parts of water at about 70 are then added, and the emulsion is further homogenized. After cooling, 100 parts of an unctuous mass having a slightly yellowish color are obtained.

Instead of 36.8 parts of the aforesaid triazine derivative, a corresponding melt consisting of equal parts of triazine derivative and parafiin wax having a melting point of 5052 may be employed.

(C) Finishing of fibrous material.-Cotton gabardine is treated on a padding machine to produce a weight increase of 100% with a bath, at 30, which contains 100 g. per liter of the emulsion prepared as in B above. After drying by hanging at room temperature, the gabardine is impregnated in a second bath with 20 parts of anhydrous sodium carbonate per liter at 30. It is thereafter dried, subjected to a heat treatment at 160 for 5 minutes, treated with dilute acetic acid, rinsed and thereafter further dried and smoothed.

'Ihe thus treated fabric, both unwashed and after it has been Washed with an aqueous solution containing 5 g. of soap and 2 g. of anhydrous sodium carbonate per liter, is water-repellent and has a softer handle than the untreated fabric.

EXAMPLE 2 (A) Preparation of the triazine c0mp0ima's.-(i) In a stirrer-type vessel provided with a dropping funnel and a thermometer, a suspension of 67 parts of cyanuric chloride in 320 parts of acetone is cooled to 0, and a solution of 100 parts of commercial stearylamine (molecular weight 276) in 2,000 parts of acetone is added drop-wise thereto in about 1 hour, the temperature being maintained between 2 and +2. On completion of the drop-wise addition, the temperature is allowed to rise to +10 and a solution of 19.2 parts of anhydrous sodium carbonate in 170 parts of water is added in the course of about 50 to 60 minutes, so that the temperature can be maintained between 10 and The mixture is thereafter allowed gradually to heat up to room temperature and is further stirred for 3 to 4 hours. The precipitated white powder is separated off and the acetone solution is evaporated to dryness in vacuo at a temperature not exceeding 40. The residue is emulsified in 1000 parts of water at about 50, suction-filtered and washed out with 2 l000 parts of cold Water on the suction filter. It is then dried in vacuo at 50 until its weight remains constant.

About 119 parts (77% of the theory) of 2-octadecylamino-4,6-dichloro-1,3,5-triazine in the form of a pale yellow powder, M.P. 71-75 is obtained.

Analysis.-Calculated: N, 13.42%; Found: N, 13.25%; Cl, 16.30%.

(ii) In a stirrer-type vessel provided with a tube for the introduction of gas, a reflux condenser and a thermometer and having a capacity of 2,000 parts by volume, 118 parts of 2-0ctadecylamino-4,6-dichloro-1,3,5-triazine, prepared as above, are dissolved in 1,000 parts of absolute alcohol, and gaseous ammonia is then introduced for 4 hours at an internal temperature of 50. In the course of the reaction, a temporary temperature rise of 6 to 7 is observed. On completion of the introduction of gaseous ammonia, the mixture is cooled to 0 to +5 and the precipitate is suction-filtered and dried at 50 in vacuo. About 102 parts of crude product are obtained.

The crude produce is recrystallized from 400 parts of benzene and the filtrate is cooled to +8 shortly before suction filtration. The product is then again dried in vacuo at 50, and about 75 parts of 2-octadecylamino-4- amino-6-chloro-1,3,5-triazine (67% of the theory) are obtained in the form of a pale yellow powder, M.P. 101103.

Analysis.--Calculated: N, 17.60%; Cl, 8.91%. Found: N, 17.41%; Cl, 8.76%.

(B) Preparation of emulsions-The procedure indicated in Example 1, under B is followed employing a melt consisting of 3.7 parts of chlorobenzene, 18.4 parts of parafiin having a melting point of 5052, and 18.4 parts of 2 octadecylamino-4-amino-6-chloro-1,3,S-triazine.

(C) Finishing of fibrous material-The procedure described under C in Example 1 is followed, and a waterrepellent fabric having a soft handle is obtained.

EXAMPLE 3 (A) Preparation of the triazine c0mp0und.-In a stirrer-type vessel having a capacity of 5,000 parts by volume and comprising a thermometer and a dropping funnel, a suspension of 67 parts of cyanuric chloride in 320 parts of acetone is cooled to 0, and there is added dropwise thereto in about 4550 minutes a solution of 113 parts of a commercial mixture of primary alkylamines, containing about 10% of stearylamine, 55% of arachidylamine and 35% of behenylamine, in 2,000 parts of acetone, the temperature being maintained between 2 and +2. On completion of the dropwise addition, the temperature is allowed to rise to +10, and a solution of 19.2 parts of anhydrous sodium carbonate in parts of water is added dropwise in 10 minutes, so that the temperature can be maintained between 10 and 15. The mixture is thereafter allowed to heat up gradually to room tmperature, and is further stirred for 3 to 4 hours. The suspension is evaporated to dryness in vacuo at a temperature not exceeding 40. The residue is recrystallized from 400 parts of benzene, cooled to +8 and immdiately suction-filtered. It is thereafter dried in vacuo at 50, and about 28.5 parts of 2-alkylamino-4,6- dichloro-'1,3,5-triazine, M.P. 96-100 are obtained of which the alkyl radicals contain mainly from 20 to 22 carbon atoms.

(B) Preparation of the emulsion and (C) Finishing of fibrous material.The procedure of Example 2 is followed, employing the alkylamino-dichlorotriazine obtained as indicated unde A. A water-repellent fabric having a soft handle is obtained.

EXAMPLE 4 (A) Preparation of the triazine c0mpound.In a stirrer-type vessel having a capacity of 2,000 parts by volume and provided with a reflux condenser and a thermometer, a suspension of 60 parts of 2-ocetadecylamino-4,6-dichloro-1,3,5-triazine and 39.7 parts of commercial stearylamine (molecular weight 276) in 1,500 parts of acetone and 500 parts of benzene is stirred for 5 hours at boiling temperature (about 55) under reflux. The mixture is thereafter cooled to room temperature and suction-filtered. The crude product is recrystallized in the moist state from 500 parts of benzene, cooled to +8 and immediately filtered off. The product is dried in 7 vacuo at 50 and about 57 parts (62% of the theory) of 2,4-di-(octadecylamino)-6-chloro-1,3,5-triazine, M.P. 133-135 are obtained.

(B) Preparation of the emulsion and (C) Finishing of fibrous materiaL-An emulsion is prepared from 2,4-di- (octadecylamino)-6-chloro-1,3,5-triazine using the method described in Example 213. A woven fabric treated therewith using the method of Example 1C is water-repellent and possesses a soft handle.

EXAMPLE 5 Emulsions are prepared, employing the triazine compounds described in Examples 2, 3 and 4. The procedure indicated under B in Example 2 is followed, but 30 parts of a gelatine solution are employed instead of the polyvinyl alcohol solution, and 1 part of sodium borate is added to the 26 parts of water at 70 which are finally to be added. Very fine emulsionssometimes in the form of pastesare obtained, which can be diluted with Water.

Similar emulsions are obtained when sodium diphosphate is added instead of sodium borate.

For the production of a soft handle and a water-repellent finish, these emulsions are employed in accordance with the method described in Example 10.

EXAMPLE 6 Highly colloidal emulsions suitable for water-proofing and for the production of a soft handle in accordance with the method of Example 1C are prepared by the method of Example 1B but replacing the polyvinyl alcohol by the same quantity of a 10% gelatine solution, and employing for the emulsification a melt consisting of 18 parts of triazine compound (see Example 1A) and 18 parts of a polyethylene glycol having a molecular Weight of 300, the formed emulsion thereafter being immediately diluted with 200 parts of water at 80.

EXAMPLE 7 In an open-stirrer type vessel, 3 parts of an emulsifier obtained by the addition of 80 mol. of ethylene oxide to 1 mol. of oleyl alcohol, and 1.2 parts of a condensation product of naphthalene sulfonic acid and formaldehyde, neutralized with aqueous sodium hydroxide solution, are heated at 80-85 with parts of a 10% gelatine solution. 9.5 parts of hot water are added, and 36 parts of a melt at 98 to 100, consisting of 12 parts each of chlorobenzene, polyethylene and the compound (2- dialkylaminol,6-dichloro-1,3,5-triazine, prepared as in Example 1) are slowly poured in. The melt is rapidly absorbed with formation of an emulsion. 26 further parts of water at to are thereafter added, and the emulsion is homogenised. A highly colloidal emulsion is obtained, which is thereafter diluted with warm water to working concentration.

Cotton poplin, treated with such an emulsion in accordance with Example 1C, exhibits a pleasant soft handle.

What is claimed is:

l. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing a 1,3,5-triazine compound of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical which contains at least 8 and at the most 22 carbon atoms, 11, p, q and r each represent a whole number of at the most 2, and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent.

2. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing polyvinyl alcohol and a 1,3,5-triazine compound of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical which contains at least 8 and at most 22 carbon atoms, and n, p, q and r each represent a Whole number of at the most 2, and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent and subsequent dry heat treatment.

3. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing gelatine and a 1,3,5-triazine compound of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical which contains at least 8 and at most 22 carbon atoms, and n, p, q and 1' each represent a whole number of at the most 2, and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent and subsequent dry heat treatment.

4. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing parafiin wax and a 1,3,5-triazine compound of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical which contains at least 8 and at most 22 carbon atoms, and n, p, q and r each represent a whole number of at the most 2, and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent and subsequent dry heat treatment.

5. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing chloroparafin Wax and a 1,3,5-triazine-compound of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical which contains at least 8 and at most 22 carbon atoms, and n, p, q and r each represent a whole number of at the most 2, and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent and subsequent dry heat treatment.

6. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing a fusible polyethylene and a 1,3,5-triazine compound of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical which contains at least 8 and at most 22 carbon atoms, and n, p, q and r each represent a whole number of at the most 2, and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent and subsequent dry heat treatment.

7. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing parafiin wax and a 1,3,5-triazine compound of the formula in which at least one and at the most two Rs represent alkyl radicals containing from 16 to 22 carbon atoms each and the remaining Rs represent hydrogen atoms, and fixing the triazine compound on the cellulose fibers by treatment with an acid binding agent and subsequent dry heat treatment.

9. A process for imparting water-repellency to cellu- W losic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing paraflin wax and the 1,3,5-triazine compound of the formula C aH /N- NO N Ill N=(3 NHz and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent and subsequent dry heat treatment.

10. A process for imparting water-repellency to cellulosic fibrous material, which comprises impregnating the fibrous material with an aqueous emulsion containing parafiin wax and the 1,3,5-triazine compound of the formula 01 1a s7 r 1 15 37 N=(|3 NH: and fixing the triazine compound on the cellulosic fibers by treatment with an acid binding agent and subsequent dry heat treatment.

11. An aqueous emulsion for imparting water-repellency to cellulosic fibrous material which contains in a finely dispersed state a 1,3,5-triazine compound of the formula in which R, R R and R each represent a bivalent aliphatic hydrocarbon radical which contains at least 8 and at the most 22 carbon atoms, and n, p, q and r each represent a whole number of at the most 2.

References Cited in the file of this patent UNITED STATES PATENTS 1,886,480 Haller Nov. 8, 1932 2,275,593 Muskat Mar. 10, 1942 2,385,765 Thurston Sept. 25, 1945 2,892,674 Sause June 30, 1959 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No 3,057 6'75 October 9, 1962 Armin Hiestand et a1, rtified that error appears in the above numbered pat- Patent should read as It is hereby ce tion and that the said Letters ent requiring correc corrected below.

" read 1uke-warm Column 4, line 70,- for "like-warn column 6, line 13 for "produce" read product 3 line 67, for "ocetadecyl" read octadecyl column 8, line 58, for "'parafin'" read paraffin Signed and sealed this 27th day of August 1963,

(SEAL) Attest:

DAVID L. LADD ERNEST W SWIDER Attesiing Officer Commissioner of Patents 

1. A PROCESS FOR IMPARTING WATER-REPELLENCY TO CELLULOSIC FIBROUS MATERIAL, WHICH COMPRISES IMPREGNATING THE FIBROUS MATERIAL WITH AN AQUEOUS EMULSION CONTAINING A 1,3,5-TRIAZINE COMPOUND OF THE FORMULA 